system of equations fails to solve

Matlab refuses to solve this system of equations despite certain other programs finding a single valid solution.

The original script:

syms x r C

eqn1 = 22.6==(x*((r^2+(1/(2*pi*5000*C)^2))^(1/2)))/(x+((r^2+(1/(2*pi*5000*C)^2))^(1/2)))

eqn2 = 19.1==(x*((r^2+(1/(2*pi*50000*C)^2))^(1/2)))/(x+((r^2+(1/(2*pi*50000*C)^2))^(1/2)))

eqn3 = 14.4==(x*((r^2+(1/(2*pi*500000*C)^2))^(1/2)))/(x+((r^2+(1/(2*pi*500000*C)^2))^(1/2)))

assume(C>0)

assume(x>0)

assume(r>0)

sol = solve(eqn1,eqn2,eqn3,x,r,C,'IgnoreAnalyticConstraints',1)

The errors:

Warning: Solutions are parameterized by the symbols: z, z1, z2. To include parameters and conditions in the solution,

specify the 'ReturnConditions' value as 'true'.

> In solve>warnIfParams (line 475)

In solve (line 357)

In failedscript (line 11)

Warning: Solutions are valid under the following conditions: 191/10 - (z*(z1^2 + 1/(10000000000*z2^2*pi^2))^(1/2))/(z

+ (z1^2 + 1/(10000000000*z2^2*pi^2))^(1/2)) == 0 & 0 < z & 0 < z1 & 0 < z2 & 72/5 - (z*(z1^2 +

4611686018427387904/(45515516623913202182151461698081*z2^2))^(1/2))/(z + (z1^2 +

4611686018427387904/(45515516623913202182151461698081*z2^2))^(1/2)) == 0 & 113/5 - (z*(z1^2 +

1/(100000000*z2^2*pi^2))^(1/2))/(z + (z1^2 + 1/(100000000*z2^2*pi^2))^(1/2)) == 0. To include parameters and

conditions in the solution, specify the 'ReturnConditions' value as 'true'.

> In solve>warnIfParams (line 482)

In solve (line 357)

In failedscript (line 11)

sol =

struct with fields:

x: [1×1 sym]

r: [1×1 sym]

C: [1×1 sym]

For simplicity the original equations are here:

Answer 1

[Sindhu Karri]

Hii,

It seems like the mathematical equations you code doesn't match with the original set of equations you provided. I urge you to recheck the equation once more. Although I wrote the code with the original equation and it seems to be working for me. You can refer to the following code. Also I recommend you to use vpasolve instead of solve function.

Code:

syms x r C

eq1=x+(1/(((1/r)^2+(2*3.14159*500*C)^2))^1/2)==22.6

eq2=x+(1/(((1/r)^2+(2*3.14159*50000*C)^2))^1/2)==19.1

eq3=x+(1/(((1/r)^2+(2*3.14159*500000*C)^2))^1/2)==14.4

assume(x>0)

assume(r>0)

assume(C>0)

sol=vpasolve(eq1,eq2,eq3,r,x,C)

https://www.mathworks.com/help/symbolic/vpasolve.html

https://www.mathworks.com/help/symbolic/solve-a-system-of-algebraic-equations.html

[Ben J Eells]

My appologies. I've been working with 2 different circuit topologies and I posted a screen clipping of the incorrect equation. I need to solve the equations that were in the original code. Here is a screen clipping of what they should look like.

I should mention I've tried vpasolve and it returns this:

struct with fields:

x: [0×1 sym]

r: [0×1 sym]

C: [0×1 sym]

Where all three components are:

Empty sym: 0-by-1

Answer 2

[Sindhu Karri]

This seems to work

syms x r C
eq1=(x*(((1/r)^2+(2*3.14159*5000*C)^2))^1/2)/(x+((((1/r)^2+(2*3.14159*5000*C)^2))^1/2))==22.6
eq2=(x*((((1/r)^2+(2*3.14159*50000*C)^2))^1/2))/(x+((((1/r)^2+(2*3.14159*5000*C)^2))^1/2))==19.1
eq3=(x*((((1/r)^2+(2*3.14159*500000*C)^2))^1/2))/(x+((((1/r)^2+(2*3.14159*5000*C)^2))^1/2))==14.4
sol=vpasolve(eq1,eq2,eq3,r,x,C)

[Ben J Eells]

I'm not sure where you're getting the 1/r term. Either that's an algebraic manipulation I'm just not seeing or a typo.

I've revised the equation a bit further after realizing Matlab may not be interpreting my input the way I had expected. Seen here:

Again there is a 1/r term in both the numerator and denominator so I suspect this is an algebraic manipulation I've forgotten over the years.

My current system of equations script looks like this:

syms x r C

eq1=(x*(sqrt((r^2)+(1/(2i*pi*5000*C))^2)))/(sqrt((x+r)^2+(1/(2i*pi*5000*C))^2))==325.3

eq2=(x*(sqrt((r^2)+(1/(2i*pi*50000*C))^2)))/(sqrt((x+r)^2+(1/(2i*pi*50000*C))^2))==282.3

eq3=(x*(sqrt((r^2)+(1/(2i*pi*500000*C))^2)))/(sqrt((x+r)^2+(1/(2i*pi*500000*C))^2))==231.8

assume(x>0)

assume(r>0)

assume(C>0)

sol=vpasolve([eq1,eq2,eq3],[r,x,C])

Again I'm getting the error:

sol =

struct with fields:

r: [0×1 sym]

x: [0×1 sym]

C: [0×1 sym]